IE9 is the mosr recent stable version of IE and IE10 is in development. WordPress.com has not supported IE7 for some time now > http://en.blog.wordpress.com/2011/05/19/just-write/
You need to upgrade your browser version and can do that here http://browsehappy.com
If you are running windows XP and cannot upgrade to IE9 then you can download a Firefox browser at that same link.

There are a lot of things on the web now that IE7 does not support, and the web is turning away from actively supporting that version so that they can implement some of the newer web technologies. Retaining support for older browsers means that developers cannot make use of the new technologies on the web. The notifications stuff from wordpress.com is one of those things that IE7 can't do.

I keep getting reminders to upgrade my browser, and I'm already using the latest IE9. It's very annoying.
And BTW I don't think it's a good idea for WP to recommend that bloggers use other browsers preferred by WP developers: it's much smarter to use the most popular browser, which is used by more viewers around the world, Internet Explorer. That way, if there are problems for your viewers who use IE, the blogger sees them too, and can fix them, or alert Support.